A generalized correspondence principle and proton-hydrogen collisions

Abstract

The Monte Carlo method is used to obtain total classical cross sections for ionization and charge transfer of hydrogen atoms in any level n by protons in the energy range 38/n2 kev to 218/n2 in the laboratory frame. The cross sections have normal statistical errors of about ±10% for ionization and ±9% or more for charge transfer. For n = 1 the classical ionization cross section agrees with experiment to within about 10 or 15 per cent over the entire range of energies, showing that the agreement between earlier classical theories of ionization and experiment is not simply the result of further dynamical approximations. The classical charge transfer cross section is somewhat higher than experiment. A generalized correspondence principle is derived which states that, for a non-relativistic quantal system of charged particles, the classically scale-invariant quantities tend to their classical values when the linear dimensions tend to infinity and other quantities are also scaled. The above cross sections are thus correct in the limit n -> [infinity]. Validity and application of the results are discussed.